\(\dfrac{x-7}{\left(x-3\right)^2-16}=\dfrac{x-7}{\left(x-3-4\right)\left(x-3+4\right)}\\=\dfrac{x-7}{\left(x-7\right)\left(x+1\right)}=\dfrac{1}{x+1} \)
\(\dfrac{x-7}{\left(x-3\right)^2-16}\)
\(=\dfrac{x-7}{\left(x-3\right)^2-4^2}\)
\(=\dfrac{x-7}{\left(x-3-4\right)\left(x-3+4\right)}\)
\(=\dfrac{x-7}{\left(x-7\right)\left(x+1\right)}\)
\(=\dfrac{1}{x+1}\)
\(\dfrac{x-7}{\left(x-3\right)^2-16}\)= \(\dfrac{x-7}{\left(x-3\right)^2-4^2}\)
= \(\dfrac{x-7}{\left(x-3-4\right)\left(x-3+4\right)}\)
= \(\dfrac{x-7}{\left(x-7\right)\left(x+1\right)}\)
=\(\dfrac{1}{x+1}\)
\(\dfrac{x-7}{\left(x-3\right)^2-16}=\dfrac{x-7}{x^2-6x+9-16}=\dfrac{x-7}{x^2-6x-7}=\dfrac{x-7}{x^2-7x+x-7}=\dfrac{x-7}{x\left(x-7\right)+\left(x-7\right)}=\dfrac{x-7}{\left(x+1\right)\left(x-7\right)}=\dfrac{1}{x+1}\)
